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The finding of multiple stellar populations (MP), defined by patterns in thestellar element abundances, is nowadays considered a distinctive feature ofglobular clusters. However, while data availability and quality improved inlast decades, this is not always true for the techniques adopted to theiranalysis, rising problems of objectivity of the claims and reproducibility.Using NGC 2808 as test case we show the use of well established statisticalclustering methods. We focus the analysis to the RGB phase, where two data setsare available from recent literature for low- and high-resolution spectroscopy.We adopt both hierarchical clustering and partition methods. We explicitlyaddress the usually neglected problem of measurement errors. The results of theclustering algorithms were subjected to silhouette width analysis to comparethe performance of the split into different number of MP. For both data setsthe results are at odd with those reported in the literature. Two MP aredetected for both data sets, while the literature reports five and four MP fromhigh- and low-resolution spectroscopy respectively. The silhouette analysissuggests that the population sub-structure is reliable for high-resolutionspectroscopy data, while the actual existence of MP is questionable for thelow-resolution spectroscopy data. The discrepancy with literature claims isexplainable due to the difference of methods adopted to MP characterisation. Bymeans of Monte Carlo simulations and multimodality statistical tests we showthat the often adopted study of the histogram of the differences in some keyelements is prone to multiple false positive findings. The adoption ofstatistically grounded methods, which adopt all the available information tosubset the data and explicitly address the problem of data uncertainty, is ofparamount importance to present more robust and reproducible researches.

astronomy and astrophysics

Robust statistical tools for identifying multiple stellar populations in  globular clusters in the presence of measurement errors. A case study: NGC  2808